The argument of 1-i3 1+i3 is: - Vidyadip

MCQ

The argument of $\frac{1-\text{i}\sqrt{3}}{1+\text{i}\sqrt{3}}$ is:

A
$60^\circ$
B
$120^\circ$
C
$210^\circ$
✓
$240^\circ$

✓

Answer

Correct option: D.

$240^\circ$

$\frac{1-\text{i}\sqrt{3}}{1+\text{i}\sqrt{3}}$
Rationalising the denominator,
$\frac{1-\text{i}\sqrt{3}}{1+\text{i}\sqrt{3}}\times\frac{1-\text{i}\sqrt{3}}{1-\text{i}\sqrt{3}}$
$=\frac{1+3\text{i}^2-2\sqrt{3}\text{i}}{1-3\text{i}^2}$
$=\frac{-2-2\sqrt{3}\text{i}}{4} \ (\because\text{i}^2=-1)$
$=\frac{-1}{2}-\text{i}\frac{\sqrt{3}}{2}$
Then, $\Rightarrow\tan\alpha=\Big|\frac{\text{Im(z)}}{\text{Re(z)}}\Big|$
$=\sqrt{3}$
$\Rightarrow\alpha=60^\circ$
Since the points $(\frac{-1}{2},-\frac{-\sqrt{3}}{2})$ lie in the third quadrant, the argument is given by:
$\theta=180^\circ+60^\circ$
$=240^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Complex Numbers and Quadratic Equations→Complex Numbers and Quadratic Equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in R$, is (where $\{.\}$ denotes fractional part function)

If the coefficients of the $(n + 1)^{th}$ term and the $(n + 3)^{th}$ term in the expansion of $(1+\text{x})^{20}$ are equal, then the value of $n$ is:

If a chord, which is not a tangent, of the parabola $y^2=16 x$ has the equation $2 x+y=p$, and midpoint $(h, k)$, then which of the following is(are) possible value(s) of $p, h$ and $k$ ?

if $\text{f(x)} = \begin{vmatrix} \cos \text{x}& \text{x} & 1\\ 2\sin \text{x} & \text{x}^{2} & 2\text{x}\ \\ \tan \text{x} & \text{x} & 1\end{vmatrix},$ then $\displaystyle \lim_{\text{x}\rightarrow 0} \dfrac {\text{f}(\text{x})}{\text{x}}.$

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is

A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed $3$ times, then the probability of getting two tails and one head is-

if $f(x) = x, x < 0: f(x) = 0, x = 0; f(x) = x, x > 0,$ then $ \lim_\limits{\text{x}\rightarrow 0}\text{f}(\text{x})$ is equal to:

If $f:R \to \left[ {0,\infty } \right)$ be such that $\mathop {{\rm{lim}}}\limits_{x \to 5} \;f\left( x \right)$ exists and $\mathop {{\rm{lim}}}\limits_{x \to 5} \frac{{{{\left( {f\left( x \right)} \right)}^2} - 9}}{{\sqrt {\left| {x - 5} \right|} }} = 0\;$,then $\mathop {{\rm{lim}}}\limits_{x \to 5} f\left( x \right)$ equals :

Let $v_1 =$ variance of $\{13, 1 6, 1 9, . . . . . , 103\}$ and $v_2 =$ variance of $\{20, 26, 32, . . . . . , 200\}$, then $v_1 : v_2$ is

The number of $5 -$tuples $(a, b, c, d, e)$ of positive integers such that

$I.$ $a, b, c, d, e$ are the measures of angles of a convex pentagon in degrees

$II$. $a \leq b \leq c \leq d \leq e$

$III.$ $a, b, c, d, e$ are in arithmetic progression is